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A fixed-order set-valued observer is presented for linear parameter-varyingsystems with bounded-norm noise and under completely unknown attack signals,which simultaneously finds bounded sets of states and unknown inputs thatinclude the true state and inputs. The proposed observer can be designed usingsemidefinite programming with LMI constraints and is optimal in the minimum\mathcal{H}_{\infty}-norm sense. We show that the strong detectability of eachconstituent linear time-invariant system is a necessary condition for theexistence of such an observer, as well as the boundedness of set-valuedestimates. Furthermore, sufficient conditions are provided for the upper boundsof the estimation errors to converge to steady state values and finally, theresults of such a set-valued observer are exhibited through an illustrativeexample.

Simultaneous input and state set-valued \mathcal{H}_{\infty}-observers for linear parameter-varying systems